Statistics Group


General information

Below are the lectures offered by our working group in the winter semester.

If you would like to write a Bachelor's or Master's thesis in Statistics, please contact Prof. Redenbach.

Important links

  • KIS: dates of the courses
  • URM: registration open till October 29th 2021 till 12 a.m..
  • OpenOLAT: course materials and further informations (access code will be given in the first lecture)

Lectures in winter term

Below are the lectures offered by our working group in the winter term 2021/2022.

Mathematical Statistics

Contents

  • Asymptotic analysis of M-estimators, especially of Maximum-Likelihood-estimators
  • Bayes and Minimax-estimators
  • Likelihood-ratio-tests: asymptotic analysis and examples (t-test, chi²-goodness-of-fit-test)
  • Glivenko-Cantelli-theorem, Kolmogorov-Smirnov-test
  • Differentiable statistic functionals and examples of applications (derivation of asymptotic results, robustness)
  • Resampling methods on the basis of Bootstrap.

Contact time

4 SWS / 60 h Lecture
2 SWS / 30 h  Tutorials

Prerequisites (Contents)

The lecture "Stochastic Methods" from the Bachelor degree program in mathematics.

Frequency of occurence

The lecture is given once per year, in the winter term.

[Link to KIS]

[Link to OLAT]

Tutorials for the lecture:

[Link to KIS]

Stochastic Methods

Contents

Grundlagen der Wahrscheinlichkeitstheorie:

  • Grundbegriffe der Wahrscheinlichkeitstheorie (Wahrscheinlichkeitsraum, Zufallsvariable, Verteilung),
  • Verteilung reellwertiger Zufallsvariablen (Binomial-, Poisson-, Exponential- und Normalverteilung u.a.),
  • Erwartungswert, Varianz, Kovarianz,
  • Verteilung von Zufallsvektoren, multivariate Normalverteilung als Beispiel,
  • Bedingte Wahrscheinlichkeit, Unabhängigkeit,
  • Gesetz der großen Zahlen,
  • Zentraler Grenzwertsatz.
    ​​​​​​​

Grundlagen der Statistik:​​​​

  • Parameterschätzer,
  • Intervallschätzer,
  • Tests.


​​​​​​​Ausblicke auf folgende Bereiche:

  • Monte-Carlo-Simulation,
  • Lineare Regression,
  • Große Datenmengen und maschinelles Lernen,
  • Markovketten.

Contact time

4 SWS / 60 h Lecture
2 SWS / 30 h  Tutorials
2 SWS / 30 h  Internship

Prerequisites (Contents)

Fundamentals of Mathematics I (Analysis and Linear Algebra).

Frequency of occurence

The lecture is given once per year, in the winter term.

[Link to KIS]

[Link to OLAT]

Tutorials for the lecture:

[Link to KIS]

Information about the practical course / lab:

[Link to KIS]

Statistical Learning for Anomaly Detection and Change-Point Analysis

Contents

  • Basics of machine/statistical learning,
  • Classifiers in the context of anomality detection:
    • logistic regression,
    • neural networks,
    • classification and regression trees (CART),
    • other methods, e.g. random forest, support vector machines (SVMs),
  • Outlier detection:
    • isolation forest,
    • one-class SVM,
    • other methods, e.g. local outlier factor (LOF),
  • Change-point detection:
    • cumulative sum (CUSUM), moving sum (MOSUM),
    • binary segmentation,
    • other methods, e.g. pruned exact olinear time (PELT) change-point detection method.

The methods are explained and evaluated using selected examples.

Contact time

2 SWS / 30 h Lecture

Prerequisites (Contents)

Classical regression analysis, e.g. from the module "Regression and Time Series Analysis".

Frequency of occurence

The lecture is given irregularly.

[Link to KIS]

[Link to OLAT will follow]

Courses for students of other departments

Here you can find more  lectures for students of other departments:

  • Mathematics/Biostatistics 1
  • Introduction to Stochastic Modeling of Cognitive Processes
  • Mathematics for Economists
  • etc.

Internships

Subjects for internships are presented at the Fachpraktikumsbörse at the end of each semester.

Reading Course

The Reading Course serves as preparation for the Master's thesis. The assignment of topics takes place individually. Please contact Prof. Redenbach if you would like to take a Reading Course in Statistics.

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